Question

for the right triangle below, find the measure of the angle. please show your answer to one decimal place.

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, for an angle $\theta$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, if we assume the angle we want to find is $\theta$, the side opposite to $\theta$ is $10$ and the side adjacent to $\theta$ is $12$.

Step2: Calculate the angle using the inverse tangent function

We know that $\theta = \tan^{- 1}(\frac{10}{12})$. First, calculate $\frac{10}{12}=\frac{5}{6}\approx0.833$. Then, $\theta=\tan^{-1}(0.833)$. Using a calculator, $\tan^{-1}(0.833)\approx39.8^{\circ}$

Answer:

$39.8^{\circ}$